SOLUTION: How many ways are there for four Cricketers, three Swimmers and two Athletes be stand in a line if the same type of sports persons stand together?

Question 762375: How many ways are there for four Cricketers, three Swimmers and two Athletes be stand in a line if the same type of sports persons stand together?
Answer by ramkikk66(644) (Show Source): You can put this solution on YOUR website!
Since the people of one sport should stand together, let us consider all 4 cricketers as one unit C, 3 swimmers as one unit S, 2 Athletes as one unit A.
So we have 3 units which can be arranged in 3! or 6 ways.
(CSA, CAS, ASC, ACS, SCA, SAC)
(Note: The expression n! (read as n-factorial is evaluated as 1*2*3...*n.
3! = 1*2*3 = 6)
Moreover, within each unit, the players can stand in all possible permutations.
4 cricketers can stand in 4! = 24 ways
3 swimmers can stand in 3! = 6 ways
2 swimmers can stand in 2! = 2 ways.
Hence the total number of ways = 6*24*6*2 = 1728 ways.
Hope this helps.
:)
RELATED QUESTIONS
There are 8 swimmers competing in a race. Prizes are awarded for the swimmers who finish... (answered by ewatrrr)

Eight people are to form two queues of four. In how many ways can this be done if: a)... (answered by Edwin McCravy)

There are four times as many swimmers as non swimmers . If there are twenty people in the (answered by Cromlix)

A group consisting of 3 boys and 2 girls is to line-up in a row for a photograph. In how... (answered by sudhanshu_kmr)

eight swimmers are competing in a race. how many ways can the swimmers fill the top three (answered by ewatrrr)

How many ways are there for 5 men and seven women to stand in a line so that three women (answered by ikleyn)

Three men and four women are to line up for a picture with the three men in the middle.... (answered by Edwin McCravy)

A class consists of 12 boys and 15 girls. How many different committees of four can be... (answered by ikleyn)

There are 7 juniors and 11 seinors on a swim team. Out of these swimmers, 4 co-captains... (answered by ewatrrr)